I didn't read the page -- I assumed it was either a "verify your email" or "authentication failed" page of some sort, so I entered my Gmail email address and password. (No, I didn't enter my Gmail password. Read below.)
There is REALLY easy-to-miss "skip" link (I forget the exact text) on the page, but the page looks so much like a login window or "verify your address" window or some other window like that that you don't realize it (and think the "skip" link is probably saying something typical like "Forgot your password?"), so you go ahead and type your credentials -- even though you've already logged in.
The only thing that saved me was the fact that Google asked me if I wanted to "Allow Access" or not, and that made my heart skip a beat and I finally realized what had happened. Thanks Google.
The scary part is that you DON'T have to type in your Google password for this to work! In fact, I typed in my LinkedIn password (I'm not quite stupid enough to type in my Google password on LinkedIn's website) -- but Google still popped up a window asking me for permission, because I was already logged into Google and it didn't even bother checking my password.
So LinkedIn almost got my permission without me ever entering my Gmail password... I almost granted access (thinking it might have been an OpenID thing) before I came to my senses and thought, WTF just happened right now?! Hell no!